Sommerfeld-Watson representation for double-spectral functions - II. Crossing symmetric pion-pion scattering amplitude without Regge poles

J. S. Frederiksen

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Abstract

We discuss, for the case of pion-pion scattering, a closed system of equations which may be used for a self-consistent calculation of partial-wave amplitudes. It is shown that, for a given sufficiently small input function, the equations have a locally unique solution in a particular Banach space of doubly Hölder continuous partial wave amplitudes. At a fixed point, the scattering amplitude is shown to satisfy both a crossing symmetric unsubtracted Mandelstam representation and the elastic unitarity condition. In this initial study the partial-wave amplitudes are holomorphic in the right half complex angular-momentum plane.

Original languageEnglish
Pages (from-to)1-16
Number of pages16
JournalCommunications in Mathematical Physics
Volume43
Issue number1
DOIs
Publication statusPublished - Feb 1975
Externally publishedYes

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